# Marginal Rate of Substitution

Imagine you are to choose between eating burgers and eating hot dogs in a week for a month. The rule is that any combination between burgers and hot dogs should make you equally happy. Initially, you might consume ten hot dogs and two burgers. However, if you've had enough hot dogs and decide to consume six hot dogs and three burgers, you are willing to give away four hot dogs per burger—the marginal rate of substitution measures that.

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The marginal rate of substitution measures the maximum number of hot dogs you are willing to give away to consume an additional burger while being equally satisfied. What happens to your marginal rate of substitution when you are willing to give away only two hot dogs in exchange for a burger? Why is the marginal rate of substitution important in economics? We will find answers to these questions and more. We will calculate the marginal rate of substitution using its formula and work on some examples!

Why don't you read on and find out the answers to these questions and all there is to know about the marginal rate of substitution?

## Marginal Rate of Substitution Definition

The marginal rate of substitution (MRS) is the rate at which a person is willing to give up one good for another good while keeping the same level of satisfaction. In simpler terms, it measures the amount of one thing someone is willing to trade for a little more or less of another thing. For instance, how many apples someone is willing to give up for one more orange.

The marginal rate of substitution is the maximum amount of a certain good an individual is willing to exchange for receiving an additional unit of another good, while maintaining the same level of utility or satisfaction.

For example, Anna has to make a choice between consuming a certain amount of clothes and a certain amount of food. She has to make a trade-off between consuming clothes and consuming food.

The marginal rate of substitution for Anna is the maximum amount of food Anna is willing to give up to obtain an additional unit of clothing. If Anna is ready to give up two meals a day to buy a Gucci bag, then Anna's marginal rate of substitution is two meals per Gucci bag.

The marginal rate of substitution is one of the essential parts of contemporary consumer behavior theory.

One of the critical assumptions of the marginal rate of substitution hypothesis is that trade-offs made between two items that an individual substitutes for one another does not affect their utility.

That is to say that regardless of what combination they choose and the amount of trade-off of one item they exchange for another, it does not affect their overall satisfaction with consumption.

When consumption levels are at equilibrium, marginal rates of substitution are equivalent to one another, and indifference curves are used to determine marginal rates of substitution between commodity bundles.

An indifference curve is a kind of graph that is used to illustrate the many combinations of two distinct goods that provide customers with the same level of utility and pleasure.

### Marginal Rate of Substitution: Indifference Curve

Your preferences affect the number of goods you consume. You might prefer consuming more pizza than pasta, or you might like drinking more Cola than eating Salad, or vice-versa. When provided with choices between two bundles, an individual will choose based on their preferences.

If the two bundles provide the same level of satisfaction to the customer, we say that the customer is indifferent between the two bundles. The marginal rate of substitution of one good for another is measured by moving along an indifference curve.

The indifference curve is a curve that shows different consumption bundles that all provide the same amount of utility to the customer.

Fig 1. - Indifference curve

Figure 1 above shows the indifference curve of an individual consuming coffee and Pepsi. Along the indifference curve, there are many choices an individual makes between specific units of coffee and certain units of Pepsi.

For example, at Point 1, an individual may choose to consume eight coffees and two units of Pepsi in a week. At Point 2 in the graph, the individual is equally satisfied with consuming four units of coffee and seven units of Pepsi in a week.

Keep in mind that these combinations between coffee and Pepsi make the consumer equally satisfied. Whether the consumer chooses the combination of coffee and Pepsi at Point 1 or at Point 2, they are equally happy.

But at what rate is the consumer willing to give up coffee for Pepsi? This is measured by the marginal rate of substitution, which is the rate at which an individual changes consumption of good one (coffee) for consuming an additional unit of good two (Pepsi).

The marginal rate of substitution is the slope of the indifference curve.

The indifference curve is not a straight line. That's because the marginal rate of substitution is not equal at all points of the indifference curve.

At some points of the indifference curve, an individual might be willing to give up more coffee in exchange for an additional unit of Pepsi. However, later on, as an individual is already receiving enough units of Pepsi, they are not willing to give up as many units of coffee. The rate at which a consumer is ready to trade coffee for Pepsi depends on the amount of Pepsi and the sugar intake they've already had. Thus, the marginal rate of substitution diminishes as we go down the indifference curve.

## Marginal Rate of Substitution Slope

To understand the marginal rate of substitution slope, we will use the indifference curve of an individual that consumes coffee and Pepsi. The individual makes different combinations of coffee and Pepsi to varying points of the indifference curve.

When the marginal rate of substitution is 3, it means that the individual is willing to give three units of coffee per one unit of Pepsi.

The MRS also measures the value an individual attaches to the consumption of one good in terms of the other. When the MRS is three, the individual clearly values Pepsi more than he values the consumption of coffee.

Fig 2. - Marginal rate of substitution along the indifference curve

Figure 2 above shows the indifference curve of an individual choosing between coffee and Pepsi. Coffee is on the vertical axis, and Pepsi is on the horizontal axis.

In our article, we consider the MRS as the rate which measures how many goods on the vertical axis an individual gives away for consuming an additional good on the horizontal axis.

### Diminishing Marginal Rate of Substitution

Notice that at different points, the MRS begins to drop. Initially, the MRS is 5, meaning five units of coffee per unit of Pepsi. Then the MRS at another point is 3, meaning 3 units of coffee are exchanged per additional unit of Pepsi. Moving down the indifference curve, the marginal rate of substitution declines.

Consumer preferences are affected by a diminishing marginal rate of substitution. That means that throughout the indifference curve, the MRS will fall.

The diminishing marginal rate of substitution is why the indifference curve is convex (bowed inward).

The MRS might be expressed as

$$-\frac{\Delta\hbox{C}}{\Delta\hbox{P}}$$

$$\hbox{Where:}$$

$$\Delta \hbox{C} = \hbox{Change in consumption of coffee}$$

$$\Delta \hbox{P} = \hbox{Change in consumption of Pepsi}$$

Due to the change in consumption of coffee being negative, we add the minus sign to make the MRS positive.

For the indifference curve to be convex, it means that the slope of the MRS should increase. That means that the change in the consumption of coffee becomes less and less negative.

As more and more Pepsi is consumed, an individual will prefer to give up fewer and fewer units of coffee to consume an additional unit of Pepsi.

As the consumption of one good in terms of another increase, the magnitude of the slope of the MRS decreases.

### Constant Marginal Rate of Substitution

Constant Marginal Rate of Substitution (MRS) describes a situation where the rate at which a consumer is willing to exchange one good for another remains constant, regardless of how much of each good they have. This means that the slope of the indifference curve, which represents the different combinations of goods that yield the same level of satisfaction to the consumer, is represented by a straight line with a constant slope.

For example, suppose that a person always wants to have a 2:1 ratio of apples to oranges to be equally satisfied. If they currently have 4 apples and 2 oranges, they would be willing to trade 2 apples for 1 orange to maintain that ratio. But if they had 10 apples and 5 oranges, they would still be willing to trade 2 apples for 1 orange, even though they have more of each. This indicates that their MRS of apples for oranges is constant at 2:1, regardless of the quantity of each good they have.

## Marginal Rate of Substitution Formula

We calculate the marginal rate of substitution by dividing the change of the first good by the change of the second good. The MRS formula is:

$$MRS = -\frac{\Delta\hbox{Good 1}}{\Delta\hbox{Good 2}}$$

The minus sign is added to make the MRS positive. As an individual gives away more of Good 1 to consume Good 2, the difference in Good 1 is always negative.

### How to Calculate the Marginal Rate of Substitution?

Let's calculate the marginal rate of substitution by following the example below.

For example, if at some point an individual moves from consuming 5 units of Good 1 to 3 units of Good 1, in order to consume an additional unit of Good 2, the difference in Good 1 is $$3-5=-2$$.

The negative sign which is added to the formula makes the MRS a positive number.

## Marginal Rate of Substitution Example

Let's look at a marginal rate of substitution example. The marginal rate of substitution reveals how we choose to consume between different combinations of two goods while keeping the same satisfaction.

Imagine you have to choose between buying clothes and food. Although you enjoy shopping, you also realize that food is important! That is why initially your MRS is 6. That means you are willing to give away six units of clothes to consume an additional unit of food. There is a certain point that you'll reach where you are not willing to consume more food; you also have to watch out for your calories.

At that point, your MRS drops to 2, meaning you are willing to give two units of clothing to consume an additional unit of food. At this point, you attach less value to food and more value to clothing.

## Marginal Rate of Substitution Importance

The marginal rate of substitution (MRS) is the rate at which consumers are willing to switch from one item or service to another. The importance of the marginal rate of substitution comes from its ability to reveal and measure whether a consumer would exchange one product or service for another one.

Companies can plot the MRS curve for their consumers, use it to forecast their sales, and accordingly make decisions on production capacity.

For example, a fast-food chain restaurant might use the MRS to determine how many hot dogs a consumer is willing to give away to consume an additional burger. This would then reveal the value consumers attach to hot dogs in terms of burgers.

If the MRS is low, meaning that consumers are willing to give fewer hot dogs per burger, it means that consumers are attaching more value to hot dogs, and that's probably where the restaurant should focus its strategy.

On the other hand, if the MRS is high, it means that consumers are willing to give away more hot dogs to consume an additional burger, hence, attaching more value to burgers.

## Marginal Rate of Substitution - Key takeaways

• The marginal rate of substitution is the maximum amount of a certain good an individual is willing to exchange for receiving an additional unit of another good.
• An indifference curve is a kind of graph that is used to illustrate the many combinations of two distinct goods that provide customers with the same level of utility and pleasure.
• The marginal rate of substitution is the slope of the indifference curve.
• MRS formula is $$MRS = -\frac{\Delta\hbox{Good 1}}{\Delta\hbox{Good 2}}$$

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##### Frequently Asked Questions about Marginal Rate of Substitution

How do you find marginal substitution rate?

You find the marginal rate of substitution by using the formula MRS= - (Change in good 1)/(Change in good 2)

What is the formula of marginal rate of  substitution?

The formula of the marginal rate of substitution is

MRS= - (Change in good 1)/(Change in good 2)

What is the marginal rate of substitution?

The marginal rate of substitution (MRS) is the rate at which a person is willing to give up one good for another good while keeping the same level of satisfaction

Why is marginal rate of substitution important?

The importance of the marginal rate of substitution comes from its ability to reveal and measure whether a consumer would exchange one product or service for another one.

What are the drawbacks of Marginal Rate of Substitution?

The drawback of the MRS is that it reveals how a consumer chooses only between two goods.

What is the slope of MRS curve?

The MRS is the slope of the indifference curve.

## Test your knowledge with multiple choice flashcards

One of the critical assumptions of the marginal rate of substitution hypothesis is that trade-offs made between two items that an individual substitutes for one another does ________ their utility.

When an individual moves from consuming 10 units of coffee and 1 unit of pepsi, to consuming 5 units of coffee and 2 units of pepsi, the MRS equals ______ .

When an individual moves from consuming 5 units of coffee and 2 unit of pepsi, to consuming 3 units of coffee and 3 units of pepsi, the MRS equals ______ .

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